Question

A monopolist faces a market (inverse) demand curve P = 50 − Q . Its total cost is C = 100 + 10Q + Q2 .

a. (1 point) What is the competitive equilibrium benchmark in this market? What profit does the firm earn if it produces at this point?

b. (2 points) What is the monopoly equilibrium price and quantity? What profit does the firm earn if it produces at this point?

c. (2 points) What is the deadweight loss at the monopoly outcome?

d. (2 points) If we implement some form of regulation here (don’t worry about different forms of pricing and rate structure yet, just stick with the basic model), what would the welfare- maximizing regulated price and quantity be? What is deadweight loss at that point?

e. (1 point) Why is there still deadweight loss at the regulated outcome?

f. (2 points) Draw a graph illustrating your answers (hint: feel free to freehand-draw the AC curve, don’t spend too much effort calculating it).

Answer 1

Hello!

a) To find the competitive equilibrium benchmark e.i. equilibrium price and quantity in a competitive market, we need to equate the price and marginal cost (MC = P). In order to find the market cost, differentiate the total cost w.r.t. the quantity.

  
  
Now, Demand is given by
Equating demand and marginal cost,



Subsituting this in the demand equation to get the competitive price.




Profit = Total Revenue - Total cost






b) To find monopoly equilibrium price and quantity, equate marginal revenue and marginal cost.
Marginal Revenue,
Here, TR = PQ = (50 - Q)*Q
TR = 50Q - Q²
MR = 50 - 2Q
We have already calculated MC = 2Q + 10

Equating MR and MC,
50 - 2Q = 2Q + 10
50 - 10 = 4Q
40 = 4Q
Q = 10
Substituting this monopoly quantity into Demand function and calculating monopoly equilibrium price,
P = 50 - Q
P = 50 - 10
P = 40

Profit = Total Revenue - Total Cost
Total Revenue = P*Q
= 40*10 = 400
Total Cost = Q² + 10Q + 100
= (10)² + 10*10 + 100
= 100 + 100 + 100 = 300
Therefore, Monopoly Profit = 400 - 300
= 100

c) Deadeight loss in the monopoly case is the loss of welfare in the soceity due to the higher price charged by the monopolist as there will be people who are willing to pay more than the cost of production but are still unable to buy the commodity. Whereas, in perfect competition, these people were able to buy the commodity as price was charged there equal to the marginal cost.  


DWL formula = 1/2* (P - MC)* (Qc - Qm) [Derived by using area of the triangle in the above diagram i.e. 1/2 X Base X Height ]
DWL = 0.5* (40 - 110/3)* (40/3 - 10)
= 0.5* ([120 - 110]/3)* ([40-30]/3)
= 0.5* 10/3* 10/3
DWL = 100/18 = 5.55

d) The welfare is maximized at the point where government puts a regulation on the monopolist to charge the price equal to the marginal cost i.e. P=MC. This is the same case of perfect competition. Here, the P will be 110/3 and Q will come out to be 40/3. Since the price is charged equal to the marginal cost, there will be no deadweight loss.

e) If the government regulates the monopolist to charge the price equal to the average total cost and not the marginal cost (or any other price higher than the marginal cost), then there will still be deadweight loss in the economy as the welfare would not be maximized.